<header>
    变换公式及其推导过程
</header>
<h2>
    推导
</h2>
<img src="./images/trigonometric-function-table.jpeg">
<p>
    由上图可以轻松得出最基本的两个公式：
</p>
<ul>
    <li>
        <code>
            ["join","sin(α+β) = cosαsinβ + sinαcosβ"]
        </code>
    </li>
    <li>
        <code>
            ["join","cos(α+β) = cosαcosβ - sinαsinβ"]
        </code>
    </li>
</ul>
<h2>
    快速查询
</h2>
<h3>
    相乘
</h3>
<ul>
    <li>
        <code>
            ["join","sinαsinβ = -",["division","1","2"],"[cos(α+β) - cos(α-β)]"]
        </code>
    </li>
    <li>
        <code>
            ["join","cosαcosβ = ",["division","1","2"],"[cos(α+β) + cos(α-β)]"]
        </code>
    </li>
    <li>
        <code>
            ["join","sinαcosβ = ",["division","1","2"],"[sin(α+β) + sin(α-β)]"]
        </code>
    </li>
    <li>
        <code>
            ["join","cosαsinβ = ",["division","1","2"],"[sin(α+β) - sin(α-β)]"]
        </code>
    </li>
</ul>
<h3>
    相加
</h3>
<ul>
    <li>
        <code>
            ["join","sinα + sinβ = 2sin",["division","α+β","2"],"cos",["division","α-β","2"]]
       </code>
    </li>
    <li>
        <code>
            ["join","sinα - sinβ = 2cos",["division","α+β","2"],"sin",["division","α-β","2"]]
       </code>
    </li>
    <li>
        <code>
            ["join","cosα + cosβ = 2cos",["division","α+β","2"],"cos",["division","α-β","2"]]
       </code>
    </li>
    <li>
        <code>
            ["join","cosα - cosβ = -2sin",["division","α+β","2"],"sin",["division","α-β","2"]]
       </code>
    </li>
</ul>
<h3>
    半角公式
</h3>
<ul>
    <li>
        <code>
            ["join","sin",["division","α","2"]," = ±",["gen",["division","1-cosα","2"]]]
        </code>
    </li>
    <li>
        <code>
            ["join","cos",["division","α","2"]," = ±",["gen",["division","1+cosα","2"]]]
        </code>
    </li>
</ul>